Various designs of such hair-cutting appliances are known, in which the combination of a blade intended for cutting and a row of teeth makes it possible, by guiding the applicance through the hair, for the hair to be lined up by the row of teeth in the working direction of the appliance, in the spaces between the teeth, and to be cut by the cutting edge of the blade which is exposed in the spaces. Since the teeth may be set to project selectively by various amounts beyond the cutting edge of the blade, it is possible to operate with the cutting edge at various distances from the scalp. This provides different lengths of cut, from thinning of the hair to shaving the neck. In one known appliance, the different distances between the tips of the teeth and the cutting edge of the blade are obtained by changing over a part of the housing, the opposing edges of which comprise rows of teeth of different lengths, the housing-part being assembled to a similar second housing-part, and the blade being secured between the two parts. In another known appliance of this kind, a part comprising a row of teeth is pushed back and forth in relation to the blade.